Question

As part of a physics experiment, a ball is catapulted upward. The height of

the ball is h(t)= -5t²+30t+5 , where t is in seconds and the height of the ball is measured in meters. What was the ball's average velocity
between t=1 andt=2?

Answer 1

To find the average velocity of the ball between t = 1 and t = 2, we need to calculate the displacement of the ball during that time interval and divide it by the duration.

The displacement of an object can be determined by finding the difference in its position at the beginning and end of the interval. In this case, we can find the height of the ball at t = 1 and t = 2 using the given equation:

h(1) = -5(1)² + 30(1) + 5

= -5 + 30 + 5

= 30 meters

h(2) = -5(2)² + 30(2) + 5

= -20 + 60 + 5

= 45 meters

The displacement of the ball between t = 1 and t = 2 is:

Displacement = h(2) - h(1)

= 45 - 30

= 15 meters

The duration of the interval is 2 - 1 = 1 second.

Finally, we can calculate the average velocity using the formula:

Average velocity = Displacement / Duration

= 15 meters / 1 second

= 15 m/s

Therefore, the average velocity of the ball between t = 1 and t = 2 is 15 m/s.